# Deep unrolling for learning optimal spatially varying regularisation parameters for Total Generalised Variation

arXiv: https://arxiv.org/abs/2502.16532 · HTML: https://mlsanity.com/paper/2502.16532/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 23 Feb 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [SeaTurtleID2022: A long-span dataset for reliable sea turtle re-identification](https://mlsanity.com/paper/2211.10307/) (2022)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Bilevel approaches for learning of variational imaging models](https://mlsanity.com/paper/1505.02120/) (2015)
- [Higher-order total variation approaches and generalisations](https://mlsanity.com/paper/1912.01587/) (2019)
- [Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling](https://mlsanity.com/paper/2301.05888/) (2023)
- [Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization](https://mlsanity.com/paper/2002.05614/) (2020)
- [Asymptotic behaviour of total generalised variation](https://mlsanity.com/paper/1502.06933/) (2015)
- [A function space framework for structural total variation regularization with applications in inverse problems](https://mlsanity.com/paper/1710.01527/) (2017)
- [Dyadic partition-based training schemes for TV/TGV denoising](https://mlsanity.com/paper/2305.07150/) (2023)

## Built on by (most cited first, 3 of 3)

- [Learning Spatially Adaptive ℓ1-Norms Weights for Convolutional Synthesis Regularization](https://mlsanity.com/paper/2503.09483/) (2025)
- [Oracle Supervision Transfers for Hyperparameter Prediction in Model-Based Image Denoising](https://mlsanity.com/paper/2605.20479/) (2026)
- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional neural network (CNN) inferring the two spatially varying TGV parameters with an unrolled algorithmic scheme that solves the corresponding variational problem. The two subnetworks are jointly trained end-to-end in a supervised fashion and as such the CNN learns to compute those parameters that drive the reconstructed images as close to the ground truth as possible. Numerical results in image denoising and MRI reconstruction show a significant qualitative and quantitative improvement compared to the best TGV scalar parameter case as well as to other approaches employing spatially varying parameters computed by unsupervised methods. We also observe that the inferred spatially varying parameter maps have a consistent structure near the image edges, asking for further theoretical investigations. In particular, the parameter that weighs the first-order TGV term has a triple-edge structure with alternating high-low-high values whereas the one that weighs the second-order term attains small values in a large neighbourhood around the edges.